REPUBLICAN PRESIDENTIAL nominee Mitt Romney is specific about how much he will cut income tax rates for every American: by one-fifth. But he is vague about how he’ll pay for this, though he insists he can cut rates without losing revenue.

The danger is a repeat of 2001 and 2003, when President Bush and Congress enacted tax cuts that plunged the nation into debt. Mr. Romney says he can prevent a repeat by closing loopholes. But the “loopholes” that cost the Treasury most are deductions and other provisions that Americans have become rather attached to — for example, measures that promote homeownership, charitable giving and employer-provided health insurance.

Which would he take away? Speaking Sunday on NBC’s “Meet the Press,” Mr. Romney offered a new twist to his non-answer. The nominee repeated that he would “limit deductions and exemptions for people at the high end,” while he would “lower the burden on middle-income people.” Asked by host David Gregory about studies showing that the math doesn’t add up — the most authoritative is from the Tax Policy Center, a joint venture of the Brookings Institution and the Urban Institute — Mr. Romney cited studies from Harvard and Princeton universities that he said prove his point.

A campaign spokeswoman told us that the Harvard study is an analysis by economist Martin Feldstein that we’ve written about previously. Mr. Feldstein showed that the Romney math might work if you strip all households with taxable income of $100,000 or more of every dollar of deduction for charitable giving, state and local income tax and mortgage interest. Does Mr. Romney favor such a plan? Would he consider such a proposal to be lowering the burden on middle-income people, even though millionaires would get a break while those in the $100,000 to $200,000 income range would pay more? He won’t say.

The Princeton study, his spokeswoman told us, refers to an analysis by economist Harvey S. Rosen. Mr. Rosen makes his math work by taking away a lot of the same deductions from the same taxpayers, plus interest-free municipal bonds and the tax break for employer-provided health care — and then assuming that economic growth will be 3 percentage points higher than it would have been without tax reform.

Mr. Rosen acknowledges that assuming increased growth runs counter to how the Treasury Department or the congressional Joint Committee on Taxation evaluate such proposals, but he says most economists agree that tax simplification would stimulate growth. “It seems odd to assume away possible increases in incomes associated with a given tax reform proposal when its explicit goal is to enhance growth,” he wrote.

The problem is that goals and results may not mesh. “In the context of revenue-neutral tax reform, any positive growth effects are likely to be small,” the Tax Policy Center economists warned. Maybe they’re wrong and Mr. Rosen is right, but is Mr. Romney going to risk the nation’s finances on that bet? There’s a reason Congress doesn’t count on “dynamic scoring,” also known as wishful thinking. More to the point, could Mr. Romney get far enough to test the proposition — would he persuade Congress to take away every popular deduction from households making $100,000 or more?

“I’ve demonstrated that I have the capacity to balance budgets,” Mr. Romney said Sunday. That would be more reassuring if he were willing to show the country a plan.